Math 2: Ratios, Unit Rates, and Proportions

Front

What is a ratio?

Back

A ratio is a comparison of two quantities that shows the relative size of one quantity to another, often expressed as 'a to b' or a:b.

Front

How do you write a proportion?

Back

A proportion is an equation that states that two ratios are equal, typically written as a/b = c/d.

Front

What is a unit rate?

Back

A unit rate is a ratio that compares a quantity to one unit of another quantity, often expressed as 'x per 1 unit'.

Front

How do you find a unit rate from a total amount?

Back

To find a unit rate, divide the total amount by the number of units. For example, if you earn $60 for 8 hours of work, the unit rate is $60 ÷ 8 = $7.50 per hour.

Front

If the ratio of dogs to cats is 5 to 3 and there are 25 dogs, how many cats are there?

Back

c = 15 (using the proportion 5/3 = 25/c).

Front

Which is the better buy: a 12 ounce can for $1.92 or a 20 ounce can for $3.00?

Back

The 20 ounce can is the better buy.

Front

How do you solve for an unknown in a proportion?

Back

Cross-multiply the ratios and then solve for the unknown. For example, if a/b = c/d, then a*d = b*c.

Front

What is the formula to find the total amount based on a unit rate?

Back

Total Amount = Unit Rate × Number of Units.

Front

If water flows at a rate of 5 gallons every 25 seconds, how many gallons flow in 45 seconds?

Back

9 gallons (using the unit rate of 0.2 gallons per second).

Front

In a recipe, if the ratio of milk to flour is 1:3 and you use 5 cups of flour, how much milk do you need?

Back

1.5 cups of milk (keeping the ratio 1:3).